Final answer:
The correct conclusion from P(G|H) = P(G) is that events G and H are independent events, represented by answer choice D. For events G and E to be mutually exclusive, P(G AND E) must be zero.
Step-by-step explanation:
If the probability of event G given event H is the same as the probability of G alone, P(G|H) = P(G), the correct conclusion is that events G and H are independent events. This is because the probability of G occurring does not change regardless of whether H has occurred or not. In other words, the occurrence of H does not influence the likelihood of G happening, which defines independence between events. Answer choice D is correct.
Furthermore, when two events G and E are described, the probabilities and their relationship can clarify if they are mutually exclusive or not. For two events to be mutually exclusive, the probability of both G and E occurring together, P(G AND E), would be zero. This numerical justification is required to confirm that the intersection of G and E is impossible, and therefore they are mutually exclusive.